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IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns

In the single-index (market) model R_i = alpha_i + beta_i R_M + e_i, which assumption is made about the residual term e_i?

The residual in the single-index model has zero mean and is uncorrelated with the market return and with other securities' residuals. Therefore securities co-move only through their common exposure to the market factor, which keeps the covariance structure simple.

  1. AIt is perfectly correlated with the market return R_M
  2. BIt has zero mean and is uncorrelated with R_M and with the residuals of other securitiesCorrect
  3. CIt has a variance equal to the market variance
  4. DIt has a mean equal to the risk-free rate
  5. It is identical for all securities in the same sector

Explanation

The single-index model assumes the residual has zero mean and is uncorrelated with the market return and with other securities' residuals. All co-movement between securities then comes through the market. The other options contradict this structure.

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